What Dark Matter should look like

Observational evidence for Dark Matter is very striking today, but its nature still
remains unclear. Currently running Dark Matter search experiments require information
on its distribution on scales far below those accessible to standard cosmological
supercomputer simulations.
Scientists at Max-Planck Institute for Astrophysics (MPA) and the
University of Groningen developed a
new ground-breaking simulation technique to make predictions on the required scales.
This allows, for the first time, to resolve small-scale Dark Matter features that are
relevant for the 'Hunt for Dark Matter'.

Fig. 1:
One-dimensional fine-grained phase-space (position-velocity plot) of CDM.
CDM is lying on the thick line. The thickness of this line is given by the very small
CDM velocity dispersion. At very early times there is only one stream (Hubble flow).
When overdensities start to grow the phase-space sheet winds up as shown in the figure.
This produces different streams: at one position there are DM particles with different
velocities. At locations where the number of streams changes the CDM density is very high.
These are so called caustics.

Fig. 2:
The plot shows the number of caustics particles have passed in a spherically symmetric
halo modelled by a Hernquist profile. The red line is based on a calculation
in the exact smooth potential whereas the green line represents the GADGET result
for a simulation of a live N-body system representing the same potential.
Both curves show excellent agreement up to the softening length of the simulation,
demonstrating the very good caustic identification of the newly invented method.

Fig. 3:
Stream density decrease for different orbits in a spherically symmetric (blue) and triaxial (red)
NFW DM halo. The underlying halo model is a fit to profiles observed in cosmological
simulations. The triaxiality leads to a faster stream density decrease in the inner region
of the halo because the potential is not spherical anymore at these radii. This fast
density decrease implies that the number of DM streams expected near the solar
position should be quite high leading to a smooth velocity distribution. The spikes of
the curves correspond to points where the particles pass through a caustic.

Particle physics provides some natural Dark Matter (DM) candidates like WIMPs
(Weakly Interacting Massive Particles). Although these particles are very weakly
interacting with ordinary matter, there are direct and indirect detection experiments
possible to catch them. Direct detection is based on scattering processes of the
DM particles with other particles in a laboratory detector. Indirect detection
exploits the annihilation of DM particles. This annihilation leads to products
like gamma-rays that could be observed, for example with the recently launched GLAST satellite.
Both methods are currently used, but up to now there is no clear evidence for any detection.
Such a discovery marks a crucial test for the DM theory.

Since the DM particles are interacting only very weakly with other particles
the experiments are rather challenging and good theoretical predictions
on the expected DM distribution are needed to fine-tune them.
The scales that are probed by detection experiments are extremely small
compared to what cosmologists are used to. Both direct and indirect detection
schemes are therefore sensitive to very small-scale features in DM.
DM is supposed to be mainly cold: CDM (cold dark matter). Cold refers to the very
small primordial velocity dispersion. Therefore the dynamical evolution of CDM
produces distinct small-scale features in the form of streams and caustics (see Figure 1).
A low stream number at a given location produces a quite clumpy velocity distribution.
Caustics on the other hand lead to very high CDM densities. These features influence
the expected detector signals. For example, caustics might boost the
annihilation flux due to their high density. A low stream number on the
other hand would produce characteristic features in detectors searching for DM.

The main tool of modern cosmology to learn about cosmic structure formation and
the DM distribution are cosmological supercomputer simulations. Such simulations are
limited by computational power in terms of the number of particles they use to represent
the DM distribution. Therefore it was up to now not possible to directly resolve the required
small-scale structures.

Mark Vogelsberger, Simon White, Volker Springel (all MPA) and Amina Helmi
(University of Groningen) therefore invented a new simulation technique to resolve
these structures for the first time in current state-of-the-art N-body simulations.
The MPA scientists implemented this new technique into the current version of MPA's GADGET code,
one of the leading codes for cosmological simulations.
Figure 2 demonstrates the identification of caustics in the DM distribution
that becomes possible with this new method. It shows a calculation done for a
spherically symmetric DM halo. Plotted is the number of caustics DM particles have passed
while orbiting in the halo potential. The green line shows the simulation result revealed with the
new method whereas the red line represents the analytic result. It is quite striking how well
the two agree in terms of the passed caustic number. This demonstrates the very accurate caustic
identification of the newly invented method that can therefore be used to estimate the caustic
boost factors of the annihilation radiation.

Another application is the estimate of the DM stream number near the solar position.
From a simple halo model for the Milky Way that takes into account its radial dependent triaxial shape,
the method can be used to show that the number of streams near the solar neighbourhood
should be of the order of 100.000. The reason for this high number is the fast decrease
in stream density while the DM particles are orbiting in the halo. It turns out that
stream densities in general decrease like 1/(t/torbital)3 (see Figure 3)
in the halo, and that chaotic orbits are also expected where the stream density decreases
even faster. These low stream densities lead to the high stream number and to the
conclusion that direct detection experiments should encounter a quite smooth velocity
distribution. Therefore detectors on earth can quite safely assume a smooth DM velocity
distribution.